英文标题：
《Failure of Smooth Pasting Principle and Nonexistence of Equilibrium
Stopping Rules under Time-Inconsistency》
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作者：
Ken Seng Tan, Wei Wei, Xun Yu Zhou
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最新提交年份：
2019
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英文摘要：
This paper considers a time-inconsistent stopping problem in which the inconsistency arises from non-constant time preference rates. We show that the smooth pasting principle, the main approach that has been used to construct explicit solutions for conventional time-consistent optimal stopping problems, may fail under time-inconsistency. Specifically, we prove that the smooth pasting principle solves a time-inconsistent problem within the intra-personal game theoretic framework if and only if a certain inequality on the model primitives is satisfied. We show that the violation of this inequality can happen even for very simple non-exponential discount functions. Moreover, we demonstrate that the stopping problem does not admit any intra-personal equilibrium whenever the smooth pasting principle fails. The \"negative\" results in this paper caution blindly extending the classical approaches for time-consistent stopping problems to their time-inconsistent counterparts.
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中文摘要：
本文考虑一个时间不一致的停止问题，其中不一致性是由非常数的时间偏好率引起的。我们证明了在时间不一致的情况下，光滑粘贴原理（用于构造传统时间一致性最优停止问题显式解的主要方法）可能会失败。具体来说，我们证明了光滑粘贴原则在个人内部博弈论框架下解决了时间不一致问题，当且仅当模型基元上的某个不等式满足时。我们证明，即使对于非常简单的非指数折扣函数，也可能发生违反此不等式的情况。此外，我们证明了当平滑粘贴原则失败时，停止问题不允许任何个人内部平衡。本文中的“负面”结果提醒我们，盲目地将时间一致性停止问题的经典方法扩展到其时间不一致的对应方法。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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一级分类：Quantitative Finance 数量金融学
二级分类：Economics 经济学
分类描述：q-fin.EC is an alias for econ.GN. Economics, including micro and macro economics, international economics, theory of the firm, labor economics, and other economic topics outside finance
q-fin.ec是econ.gn的别名。经济学，包括微观和宏观经济学、国际经济学、企业理论、劳动经济学和其他金融以外的经济专题
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